Graded Lie algebras of Cartan type in characteristic 2

TL;DR

This paper studies the structure of graded Lie algebras of Cartan type in characteristic 2, identifying their simple components and exploring isomorphisms, including conjectures about type K algebras.

Contribution

It determines simple constituents and exceptional isomorphisms for Cartan type Lie algebras in characteristic 2, and proposes a conjecture for type K algebras.

Findings

Identified simple constituents of Cartan type W, S, H in characteristic 2

Discovered some exceptional isomorphisms between these algebras

Conjectured simple constituents of type K algebras are isomorphic to type H

Abstract

We investigate the graded Lie algebras of Cartan type $W$, $S$ and $H$ in characteristic 2 and determine their simple constituents and some exceptional isomorphisms between them. We also consider the graded Lie algebras of Cartan type $K$ in characteristic 2 and conjecture that their simple constituents are isomorphic to Lie algebras of type $H$.